Patriot uses SARH only for terminal approach like SM-2, so there's little warning about the attack. The radars only give away very late that the aircraft is under attack. That's one "scary" thing about it.

BAMSE was first and foremost a short range air defence with an astonishing effective ceiling claim and a cheap (command controlled) missile.

It would be a great complement to missiles with expensive seekers, but there are likely few suitable targets for BAMSE.

Everything that carries a radar/radio jammer might throw off the aim, the system requires line of sight between target and fire control radar and radar 'stealth' targets that would be easily visible in IIR might still be too hard to sense for the radars used. Finally, the fire control radar needs to keep looking at the target throughout the engagement. That's but a few seconds, but a shutdown due to ARM threat would break the engagement and the target might be able to triangulate the fire control radar during this time. That's troublesome if the target is a decoy drone with ESM specialised on triangulating radars or if the missile fails.

BAMSE is a bit of a bet; a bet that the relatively cheap system doesn't get defeated by ECM.

Other radar-centric air defence systems do similar bets, but with higher stakes and better odds.

I'm not all that familiar with Patriot's guidance properties, but (IIRC) it originally used a "Track Via Missile" concept in which the missile downlinked target data to the radar, which then provided guidance data. Presumable that's been succeeded by a newer design?